There are many improvements for improving the twisting force of a sleeve device or a spanner. In one prior art, the inner side of the sleeve (or the driving portion of the spanner) is teethed so as to increase the friction force between the inner side of the sleeve (the driving portion) and screw means located therein. However the teeth are damaged at the apexes, they cannot suffer from a larger twisting force. As it is used for a longer time, the sleeve (or spanner) will be destroyed.
In another improvement, each of the connection of two inner sides of the sleeve (or driving portion of a spanner) is formed with a recess for firmly securing the apexes of a screw means. However if a larger force is applied thereon, the apexes will be destroyed, and thus it is not an ideal design.